Using that calculator and my own tests (believe or not they prove
results given by calc) we can find out that combination of
Good-Good-Medium synergies gives the best output dmg/dps for WA/BL/FA
and Good-Medium-Bad for WI/FA/FB.

Now to the main part:
To conclude all I said before we are trying to find out which
combination of synergies will give the best output dmg and in which
cycles would it be good to use them.

Why there are 2 of them?
As we said before Good-Good-Medium (Good-Medium-Bad) synergy combination
gives the best output. We are using it at start. After pressing Fatal
Attack your synergy will be activated and you timer will begin ticking
(12 sec - BL/WI/FB; 13 sec - FA/FS; 15 sec - WA ). This time is totally
enough to reapeat Good-Good-Medium (Good-Medium-Bad) and Activate again
without losing dmg/dps.
"Hardcore" one adds one more synergy after first activation to stack
with previous one. This combo will give you just a little bit more dps
due to one more Fatal Attack In the other hand: it is harder to perform
compared boost given.

Conclusion:
Seems many words and complicated. But on practise it is easy. Find out
yours Good,Medium,Bad synergies and use "basics" or "hardcore"
combination for the best result.

P.S.
1) While mob has low hp Activation can be extended with Fatal Attack II and III to finish killing.
2) This guide was written after around 150 tests of BM3 BL on bosses with high def (Pluma/Leth/Tyrant/Manticore)
3) If you find out something that will be better, I will be pleased to add it / change in this guide.
4) All target debuffs from synergy (such as -5% def , -25% cd resist
etc) do work for rest party members. Just add this debuffing synergy
into "hardcore" instead of Medium (Good) after first activation while
you are in party. It will be more effective then 10% amp for yourself
(for example).